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Median Bernoulli Numbers and Ramanujan’s Harmonic Number Expansion [PDF]
Mathematics, 2022 Ramanujan-type harmonic number expansion was given by many authors. Some of the most well-known are: Hn∼γ+logn−∑k=1∞Bkk·nk, where Bk is the Bernoulli numbers.
Kwang-Wu Chen
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Pseudorandom number generator based on the Bernoulli map on cubic algebraic integers [PDF]
, 2018 We develop a method for generating pseudorandom binary sequences using the Bernoulli map on cubic algebraic integers. The distinguishing characteristic of our generator is that it generates chaotic true orbits of the Bernoulli map by exact computation ...
Asaki Saito, Akihiro Yamaguchi
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Asymptotics of Bernoulli random walks, bridges, excursions and meanders with a given number of peaks [PDF]
, 2007 A Bernoulli random walk is a random trajectory starting from 0 and having i.i.d. increments, each of them being $+1$ or -1, equally likely. The other families cited in the title are Bernoulli random walks under various conditionings.
Jean-Maxime Labarbe +1 more
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Journal of Fluid Science and Technology, 2016 The extended Bernoulli equation is formulated in an exact form for a microscopic and small Reynolds number Jeffery-Hamel flow in a two-dimensional convergent or divergent channel.
Toshihide FUJIKAWA +4 more
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InformationCertain methods for implementing chaotic maps can lead to dynamic degradation of the generated number sequences. To solve such a problem, we develop a method for generating pseudorandom number sequences based on multiple one-dimensional chaotic maps.
Leonardo Palacios-Luengas +5 more
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Probabilistic Interpretation of Number Operator Acting on Bernoulli Functionals
Mathematics, 2022 Let N be the number operator in the space H of real-valued square-integrable Bernoulli functionals. In this paper, we further pursue properties of N from a probabilistic perspective.
Jing Zhang, Lixia Zhang, Caishi Wang
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Demonstratio Mathematica, 2022 In this article, the authors present two identities involving products of the Bernoulli numbers, provide four alternative proofs for these two identities, derive two closed-form formulas for the Bernoulli numbers in terms of central factorial numbers of ...
Chen Xue-Yan +3 more
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On a more accurate half-discrete Hilbert-type inequality involving hyperbolic functions
Open Mathematics, 2022 In this work, by the introduction of a new kernel function composed of exponent functions with several parameters, and using the method of weight coefficient, Hermite-Hadamard’s inequality, and some other techniques of real analysis, a more accurate half-
You Minghui, Sun Xia, Fan Xiansheng
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On a new generalization of some Hilbert-type inequalities
Open Mathematics, 2021 In this work, by introducing several parameters, a new kernel function including both the homogeneous and non-homogeneous cases is constructed, and a Hilbert-type inequality related to the newly constructed kernel function is established.
You Minghui, Song Wei, Wang Xiaoyu
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New Cusa-Huygens type inequalities
AIMS Mathematics, 2020 Using the monotone form of the L'Hôspital rule, we discuss the (absolute) monotonicity of the functions $U\left(x\right)=\frac{1}{x^{4}}-% \frac{1}{x^{5}}\frac{3\sin x}{\cos x+2}$, $G(x)=\frac{1}{x^{2}}\left[\frac{% \ln\sin x-\ln x}{\ln\left(2+\cos x ...
Ling Zhu
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